On Passivity, Feedback Passivity, And Feedback Passivity Over Erasure Network: A Piecewise Affine Approximation Approach

TL;DR

This paper investigates passivity and feedback passivity of nonlinear systems using piecewise affine approximations, extending results to systems over lossy and Gilbert-Elliott channels, with derived sufficient conditions.

Contribution

It introduces a novel approach using piecewise affine approximations to analyze passivity over lossy and stochastic communication channels.

Findings

Derived sufficient conditions for passivity and feedback passivity.

Extended results to systems over Gilbert-Elliott channels.

Special case analysis for systems over lossy channels.

Abstract

In this paper, we deal with the problem of passivity and feedback passification of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for passivity and feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived.